reserve A,B,C for Category,
  F,F1 for Functor of A,B;
reserve o,m for set;
reserve t for natural_transformation of F,F1;

theorem Th28:
  for F1,F2 being Functor of A,B, G being Functor of B,C st F1
  is_naturally_transformable_to F2 for t being natural_transformation of F1,F2
  holds G*t = G*(t qua Function)
proof
  let F1,F2 be Functor of A,B, G be Functor of B,C;
  assume
A1: F1 is_naturally_transformable_to F2;
  then
A2: F1 is_transformable_to F2;
  let t be natural_transformation of F1,F2;
  thus G*t = G*(t qua transformation of F1,F2) by A1,ISOCAT_1:def 7
    .= G*(t qua Function) by A2,ISOCAT_1:def 5;
end;
